# Mark Sepanski

Professor of Mathematics

Director of Graduate Studies

** Professor of Mathematics**
**Education:**

Ph.D., M.I.T., 1990-1994 (Advisor: B. Kostant)

B.S., Purdue University, 1987-1990

**Biography:**

Dr. Sepanski joined the Baylor faculty in 1997. Prior to coming to Baylor, he had postdocs at Oklahoma State University (1995-1997) and Cornell University (1994-1995) after graduating from MIT in 1994.

Though born in Minnestoa and ending up in Indiana, he mostly grew up in Wisconsin. He has been married to Laura Sepanski since 1990 and has three delightful children: Sarah, Benjamin, and Shannon. Besides mathematics, he enjoys playing games, gardening with native Texas plants, playing the guitar, Tae Kwon Do, rock climbing, hiking, camping, biking, running, reading fantasy, spending time with his family, and cooking.

**Academic Interests and Research:**

Dr. Sepanski's research is in Lie theory and, in particular, in representation theory of real reductive Lie groups.

Dr. Sepanski has been the Director of Graduate Studies since 2010 and on the Graduate Committee since 2000.

**Selected Research Articles:**

Lyndon word decompositions and pseudo orbits on q-nary graphs, joint with R. Band and J. Harrison, J. Math. Anal. Appl., 470 (2019), no. 1, 135--144.

Schrödinger-type equations and unitary highest weight representations of the metaplectic group, joint with M. Hunziker and R. Stanke, Representation theory and harmonic analysis on symmetric spaces, 157--174, Contemp. Math., 714, Amer. Math. Soc., Providence, RI, 2018.

Net regular signed trees, joint with I. Michael, *Australas. J. Combin. 66* (2016), 192-204.

A system of Schrödinger equations and the oscillator representation, joint with M. Hunziker and R. Stanke, *Electron. J. Differential Equations 2015*, No. 260, 28 pp.

On divisibility of convolutions of central binomial coefficients, *Electron. J. Combin. 21* (2014), no. 1, Paper 1.32, 7 pp.

The minimal representation of the conformal group and classical solutions to the wave equation, joint with M. Hunziker and R. Stanke, *J. Lie Theory 22* (2012), no. 2, 301-360.

Global Lie symmetries of the heat and Schrödinger equation, joint with R. Stanke, *J. Lie Theory 20* (2010), no. 3, 543-580.

Distinguished orbits and the L-S category of simply connected compact Lie groups, joint with M. Hunziker, *Topology Appl. 156* (2009), no. 15, 2443-2451.

Positivity of zeta distributions and small unitary representations, joint with L. Barchini and R. Zierau, In: The ubiquitous heat kernel, 1-46,
*Contemp. Math. 398*, Amer. Math. Soc., Providence, RI, 2006.

On SL(2,**R**) Lie symmetries and representation theory, joint with R. Stanke, * J. Funct. Anal. 224 *(2005), 1-21.

Infinite commutative product formulas for relative extremal projectors, joint with C. Conley,
*Adv. Math. 196* (2005), 52-77.

Singular projective bases and the generalized Bol operator, joint with C. Conley,
*Adv. Appl. Math. 33* (2004), 158-191.

K-types of SU(1,n) representations and restriction of cohomology, *Pacific J. Math. 192* (2000),
385-398.

Block-compatible metaplectic cocycles, joint with W. Banks and J. Levy,
* J. Reine Angew. Math. 507* (1999), 131-163.

Closure ordering and the Kostant-Sekiguchi correspondence, joint with D. Barbasch,
*Proc. Amer. Math. Soc. 126* (1998), 311-317.

L_2(q) and the rank two Lie groups: their construction in light of Kostant's conjecture, *Trans. Amer. Math. Soc. 347* (1995), no. 10, 3983-4021.

**Books:**

*Algebra*, Pure and Applied Undergraduate Texts, 11, American Mathematical Society, 2010.

*Compact Lie Groups*, Graduate Texts in Mathematics, 235, Springer-Verlag, 2007.

**Ph.D. Students:**

- John Miller (joint with M. Hunziker)

**Teaching Interests:**

Dr. Sepanksi's teaching interests range from introductory calculus
classes for undergraduates to specialized courses for Ph.D. students.

**Courses taught at Baylor:**

- MTH 1304 - Pre-Calculus
- MTH 1321 - Calculus I
- MTH 1322 - Calculus II
- MTH 2311 - Linear Algebra
- MTH 2321 - Calculus III
- MTH 3312 - Foundations of Combinatorics and Algebra
- MTH 3323 - Introduction to Analysis
- MTH 3325 - Ordinary Differential Equations
- MTH 4314 - Abstract Algebra
- MTH 4326 - Advanced Calculus I
- MTH 4327 - Advanced Calculus II
- MTH 5310 - Advanced Abstract Algebra I
- MTH 5311 - Advanced Abstract Algebra II
- MTH 5323 - Theory of Functions of Real Variables I
- MTH 5324 - Theory of Functions of Real Variables II
- MTH 5330 - Topology
- MTH 5331 - Algebraic Topology I
- MTH 5332 - Algebraic Topology II
- MTH 5340 - Differential Geometry
- MTH 5350 - Complex Analysis
- MTH 6340 - Compact Lie Groups
- MTH 6341 - Lie Algebras
- MTH 6V43 - Advanced Topics in Representation Theory